Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24810 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2416 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#575 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,40,19,24,18,23)(14,25,28,20,30,44,29,45)(15,31,41,21,35,48,34,49)(16,36,37,22,39,64,38,50)(26,42,32,46,54,68,53,67)(27,55,56,51,58,43,57,69)(33,47,65,63,62,71,61,59)(52,70,60,74,73,75,72,66);(12,14,17,28,19,30,18,29)(13,20,23,25,24,45,40,44)(15,32,34,26,35,53,41,54)(16,27,37,56,39,58,38,57)(21,46,48,68,49,67,31,42)(22,43,36,51,50,55,64,69)(33,60,61,52,62,72,65,73)(47,70,63,74,71,75,59,66);(12,15)(13,21)(14,26)(16,33)(17,34)(18,41)(19,35)(20,42)(22,47)(23,48)(24,49)(25,46)(27,52)(28,53)(29,32)(30,54)(31,40)(36,63)(37,61)(38,65)(39,62)(43,66)(44,67)(45,68)(50,71)(51,70)(55,74)(56,72)(57,60)(58,73)(59,64)(69,75);(12,16,18,38,19,39,17,37)(13,22,40,64,24,50,23,36)(14,27,29,57,30,58,28,56)(15,33,41,65,35,62,34,61)(20,43,44,69,45,55,25,51)(21,47,31,59,49,71,48,63)(26,52,32,60,54,73,53,72)(42,66,67,75,68,74,46,70)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17798);